Problem: Rewrite as a simplified fraction. ${0.45\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 458.8888...\\ 100x &= 45.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 413}$ ${x = \dfrac{413}{900}} $